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ChemistryMediumClass 12

Solid State — Packing + Defects

Solid State

38

JEE Qs

10%

Hard

90

min

Master the r-a relationships, Z values, and packing efficiencies for all common unit cells, and understand the causes and consequences of each type of defect.

🧮 Key Formulas

Density (ρ) = (Z * M) / (a^3 * N_A)
Packing Efficiency (%) = (Volume occupied by atoms in unit cell / Total volume of unit cell) * 100
For Simple Cubic (SC): Z=1, a=2r, Packing Efficiency = 52.4%
For Body-Centered Cubic (BCC): Z=2, 4r = a * sqrt(3), Packing Efficiency = 68%
For Face-Centered Cubic (FCC) / Hexagonal Close Packing (HCP): Z=4 (for FCC), 4r = a * sqrt(2), Packing Efficiency = 74%
Number of tetrahedral voids = 2 * Z (for close-packed structures)
Number of octahedral voids = Z (for close-packed structures)
Radius ratio (r_cation / r_anion) ranges for different coordination numbers (e.g., 0.225-0.414 for tetrahedral, 0.414-0.732 for octahedral)

✅ Key Points for JEE

  • 1Accurately calculate 'Z' (number of atoms per unit cell) by correctly counting contributions from corners, faces, edges, and body center.
  • 2Visualize and relate atomic radius (r) to unit cell edge length (a) for SC, BCC, and FCC structures to calculate packing efficiency.
  • 3Understand the formation, location, and number of tetrahedral and octahedral voids in close-packed structures (FCC/HCP).
  • 4Distinguish between different types of point defects (stoichiometric: Schottky, Frenkel; non-stoichiometric: metal excess/deficiency; impurity) and their impact on density, electrical conductivity, and color.
  • 5Apply density formula correctly, ensuring consistent units for molar mass, edge length, and Avogadro's number.

⚠️ Common Mistakes

  • Incorrectly calculating the number of atoms (Z) per unit cell by miscounting contributions from different positions.
  • Confusing the coordination numbers and packing efficiencies for different crystal systems (SC, BCC, FCC/HCP).
  • Misinterpreting the effects of Schottky and Frenkel defects on the density of the crystal.
  • Struggling with 3D visualization of atoms and voids within the unit cell, leading to errors in r-a relationships or void location.

📝 Practice Questions

See all

Q66. Match List - I with List - II. Choose the correct answer from the options given below : (1) (A)-(IV), (B)-(II), (C)-(I), (D)-(III) (2) (A)-(I), (B)-(II), (C)-(III), (D)-(IV) (3) (A)-(III), (B)-(I), (C)-(IV), (D)-(II) (4) (A)-(II), (B)-(IV), (C)-(III), (D)-(I)

2025·MCQMedium

Q55.The values of conductivity of some materials at 298 .15 K in Sm−1 are 2 .1 × 103, 1 .0 × 10−16, 1 .2 × 10, 3 .91 , 1 .5 × 10−2, 1 × 10−7, 1 .0 × 103. The number of conductors among the materials is _____.

2024·NumericalEasy

Q42.The correct relationships between unit cell edge length ‘a’ and radius of sphere ‘r’ for face-centred and body- centred cubic structures respectively are: (1) 2√2r = a and √3r = 4a (2) r = 2√2a and 4r = √3a (3) r = 2√2a and √3r = 4a (4) 2√2r = a and 4r = √3a

2023·ConceptualEasy

Q45.A metal M crystallizes into two lattices :- face centred cubic (fcc) and body centred cubic (bcc) with unit cell edge length of 2. 0 and 2. 5 °A respectively. The ratio of densities of lattices fcc to bec for the metal M is _______(Nearest integer) Q46. 20% of acetic acid is dissociated when its 5 g is added to 500 mL of water. The depression in freezing point of such water is _____ × 10−3∘C. Atomic mass of C, H and O are 12, 1 and 16 a.m.u. respectively. [Given : Molal depression constant and density of water are 1. 86 K kg mol−1 and 1 g cm−3 respectively. Q47. 1 × 10−5 M AgNO3 is added to 1 L of saturated solution of AgBr. The conductivity of this solution at 298 K is _______ × 10−8 S m−1 . [Given : Ksp(AgBr) = 4. 9 × 10−13 at 298 K λ0 = 6 × 10−3 Sm2 mol−1 Ag+ JEE Main 2023 (01 Feb Shift 2) JEE Main Previous Year Paper λ0Br−= 8 × 10−3 Sm2 mol−1 λ0 = 7 × 10−3 Sm2 mol−1] NO−3

2023·NumericalMedium

Q45.Number of crystal systems from the following where body centred unit cell can be found, is _____. Cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, triclinic

2023·NumericalMedium

Q37.Which of the following represents the lattice structure of A0 . 95O containing A2 + , A3 + and O2 – ions? A. JEE Main 2023 (01 Feb Shift 1) JEE Main Previous Year Paper B. C. (1) B and C only (2) B only (3) A and B only (4) A only

2023·MCQMedium

NCERT Chapters

  • Class 12 Chemistry Ch 1: The Solid State